Methods for measuring cross-sectional areas in luminal organs

ABSTRACT

Methods for measuring cross-sectional areas in luminal organs. In at least one embodiment of a method for measuring a size parameter of a targeted treatment site of the present disclosure, the method comprises the steps of introducing an impedance device into a treatment site, the impedance device selected from the group consisting of an impedance catheter and an impedance wire; injecting a first solution of a first compound having a first conductivity into the treatment site; measuring a first conductance value at the treatment site using the impedance device, the first conductance value indicative of a bolus of the first solution, and calculating a size parameter of the treatment site based in part upon the first conductivity of the first solution, the first conductance.

PRIORITY

The present patent application is related to, claims the prioritybenefit of, and is a continuation application of, U.S. patentapplication Ser. No. 12/352,211, filed on Jan. 12, 2009 and issued asU.S. Pat. No. 8,082,032 on Dec. 20, 2011, which is related to, claimsthe priority benefit of, and is a continuation application of, U.S.patent application Ser. No. 11/891,981, filed Aug. 14, 2007, now U.S.Pat. No. 8,114,143, which is related to, claims the priority benefit of,and is a divisional application of, U.S. patent application Ser. No.10/782,149, filed Feb. 19, 2004 and issued as U.S. Pat. No. 7,454,244 onNov. 18, 2008, which is related to, claims the priority benefit of, U.S.Provisional Patent Application Ser. No. 60/449,266, filed Feb. 21, 2003,U.S. Provisional Patent Application Ser. No. 60/493,145, filed Aug. 7,2003, and U.S. Provisional Patent Application Ser. No. 60/502,139, filedSep. 11, 2003. The contents of each of these applications are herebyincorporated by reference in their entirety into this disclosure.

BACKGROUND

The present disclosure relates generally to medical diagnostics andtreatment equipment, including methods and apparatuses for measuringluminal cross-sectional area of blood vessels, heart valves and otherhollow visceral organs.

Coronary Heart Disease

Coronary heart disease is caused by atherosclerotic narrowing of thecoronary arteries. It is likely to produce angina pectoris, heart attackor both. Coronary heart disease caused 466,101 deaths in USA in 1997 andis the single leading cause of death in America today. Approximately, 12million people alive today have a history of heart attack, anginapectoris or both. The break down for males and females is 49% and 51%,respectively. This year, an estimated 1.1 million Americans will have anew or recurrent coronary attack, and more than 40% of the peopleexperiencing these attacks will die as a result. About 225,000 people ayear die of coronary attack without being hospitalized. These are suddendeaths caused by cardiac arrest, usually resulting from ventricularfibrillation. More than 400,000 Americans and 800,000 patientsworld-wide undergo a non-surgical coronary artery interventionalprocedure each year. Although only introduced in the 1990s, in somelaboratories intra-coronary stents are used in 90% of these patients.

Stents increase minimal coronary lumen diameter to a greater degree thanpercutaneous transluminal coronary angioplasty (PTCA) alone according tothe results of two randomized trials using the Palmaz-Schatz stent.These trials compared two initial treatment strategies: stenting aloneand PTCA with “stent backup” if needed. In the STRESS trial, there was asignificant difference in successful angiographic outcome in favor ofstenting (96.1% vs. 89.6%).

Intravascular Ultrasound

Currently intravascular ultrasound is the method of choice to determinethe true diameter of the diseased vessel in order to size the stentcorrectly. The term “vessel,” as used herein, refers generally to anyhollow, tubular, or luminal organ. The tomographic orientation ofultrasound enables visualization of the full 360° circumference of thevessel wall and permits direct measurements of lumen dimensions,including minimal and maximal diameter and cross-sectional area.Information from ultrasound is combined with that obtained byangiography. Because of the latticed characteristics of stents,radiographic contrast material can surround the stent, producing anangiographic appearance of a large lumen, even when the stent struts arenot in full contact with the vessel wall. A large observationalultrasound study after angio-graphically guided stent deploymentrevealed an average residual plaque area of 51% in a comparison ofminimal stent diameter with reference segment diameter, and incompletewall apposition was frequently observed. In this cohort, additionalballoon inflations resulted in a final average residual plaque area of34%, even though the final angiographic percent stenosis was negative(20.7%). These investigators used ultrasound to guide deployment.

However, using intravascular ultrasound as mentioned above requires afirst step of advancement of an ultrasound catheter and then withdrawalof the ultrasound catheter before coronary angioplasty thereby addingadditional time to the stent procedure. Furthermore, it requires anultrasound machine. This adds significant cost and time and more risk tothe procedure.

Aortic Stenosis

Aortic Stenosis (AS) is one of the major reasons for valve replacementsin adult. AS occurs when the aortic valve orifice narrows secondary tovalve degeneration. The aortic valve area is reduced to one fourth ofits normal size before it shows a hemodynamic effect. Because the areaof the normal adult valve orifice is typically 3.0 to 4.0 cm², an area0.75-1.0 cm² is usually not considered severe AS. When stenosis issevere and cardiac output is normal, the mean trans-valvular pressuregradient is generally >50 mmHg. Some patients with severe AS remainasymptomatic, whereas others with only moderate stenosis developsymptoms. Therapeutic decisions, particularly those related tocorrective surgery, are based largely on the presence or absence ofsymptoms.

The natural history of AS in the adult consists of a prolonged latentperiod in which morbidity and mortality are very low. The rate ofprogression of the stenotic lesion has been estimated in a variety ofhemodynamic studies performed largely in patients with moderate AS.Cardiac catheterization and Doppler echocardiographic studies indicatethat some patients exhibit a decrease in valve area of 0.1-0.3 cm² peryear; the average rate of change is 0.12 cm² per year. The systolicpressure gradient across the valve may increase by as much as 10 to 15mmHg per year. However, more than half of the reported patients showedlittle or no progression over a 3-9 year period. Although it appearsthat progression of AS can be more rapid in patients with degenerativecalcific disease than in those with congenital or rheumatic disease, itis not possible to predict the rate of progression in an individualpatient.

Eventually, symptoms of angina, syncope, or heart failure develop aftera long latent period, and the outlook changes dramatically. After onsetof symptoms, average survival is <2-3 years. Thus, the development ofsymptoms identifies a critical point in the natural history of AS.

Many asymptomatic patients with severe AS develop symptoms within a fewyears and require surgery. The incidence of angina, dyspnea, or syncopein asymptomatic patients with Doppler outflow velocities of 4 m/s hasbeen reported to be as high as 38% after 2 years and 79% after 3 years.Therefore, patients with severe AS require careful monitoring fordevelopment of symptoms and progressive disease.

Indications for Cardiac Catheterization

In patients with AS, the indications for cardiac catheterization andangiography are to assess the coronary circulation (to confirm theabsence of coronary artery disease) and to confirm or clarify theclinical diagnosis of AS severity. If echocardiographic data are typicalof severe isolated. AS, coronary angiography may be all that is neededbefore aortic valve replacement (AVR). Complete left- and right-heartcatheterization may be necessary to assess the hemodynamic severity ofAS if there is a discrepancy between clinical and echocardiographic dataor evidence of associated valvular or congenital disease or pulmonaryhypertension.

The pressure gradient across a stenotic valve is related to the valveorifice area and transvalvular flow through Bernoulli's principle. Thus,in the presence of depressed cardiac output, relatively low pressuregradients are frequently obtained in patients with severe AS. On theother hand, during exercise or other high-flow states, systolicgradients can be measured in minimally stenotic valves. For thesereasons, complete assessment of AS requires (1) measurement oftransvalvular flow, (2) determination of the transvalvular pressuregradient, and (3) calculation of the effective valve area. Carefulattention to detail with accurate measurements of pressure and flow isimportant, especially in patients with low cardiac output or a lowtransvalvular pressure gradient.

Problems with Current Aortic Valve Area Measurements

Patients with severe AS and low cardiac output are often present withonly modest transvalvular pressure gradients (i.e., <30 mmHg). Suchpatients can be difficult to distinguish from those with low cardiacoutput and only mild to moderate AS. In both situations, the low-flowstate and low pressure gradient contribute to a calculated effectivevalve area that can meet criteria for severe AS. The standard valve areaformula (simplified Hakki formula which is valve area=cardiacoutput/[pressure gradient]^(1/2)) is less accurate and is known tounderestimate the valve area in low-flow states; under such conditions,it should be interpreted with caution. Although valve resistance is lesssensitive to flow than valve area, resistance calculations have not beenproved to be substantially better than valve area calculations.

In patients with low gradient stenosis and what appears to be moderateto severe AS, it may be useful to determine the transvalvular pressuregradient and calculate valve area and resistance during a baseline stateand again during exercise or pharmacological (i.e., dobutamine infusion)stress. Patients who do not have true, anatomically severe stenosisexhibit an increase in the valve area during an increase in cardiacoutput. In patients with severe AS, these changes may result in acalculated valve area that is higher than the baseline calculation butthat remains in the severe range, whereas in patients without severe AS,the calculated valve area will fall outside the severe range withadministration of dobutamine and indicate that severe AS is not present.

There are many other limitations in estimating aortic valve area inpatients with aortic stenosis using echocardiography and cardiaccatheterization. Accurate measurement of the aortic valve area inpatients with aortic stenosis can be difficult in the setting of lowcardiac output or concomitant aortic or mitral regurgitations,Concomitant aortic regurgitation or low cardiac output can overestimatethe severity of aortic stenosis. Furthermore, because of the dependenceof aortic valve area calculation on cardiac output, any under oroverestimation of cardiac output will cause inaccurate measurement ofvalve area. This is particularly important in patients with tricuspidregurgitation. Falsely measured aortic valve area could causeinappropriate aortic valve surgery in patients who do not need it.

Other Visceral Organs

Visceral organs such as the gastrointestinal tract and the urinary tractserve to transport luminal contents (fluids) from one end of the organto the other end or to an absorption site. The esophagus, for example,transports swallowed material from the pharynx to the stomach. Diseasesmay affect the transport function of the organs by changing the luminalcross-sectional area, the peristalsis generated by muscle, or bychanging the tissue components. For example, strictures in the esophagusand urethra constitute a narrowing of the organ where fibrosis of thewall may occur. Strictures and narrowing can be treated with distension,much like the treatment of plaques in the coronary arteries.

BRIEF SUMMARY

The present disclosure provides for a system for measuringcross-sectional areas and pressure gradients in luminal organs. Thepresent disclosure also comprises a method and apparatus for measuringcross-sectional areas and pressure gradients in luminal organs, such as,for example, blood vessels, heart valves, and other visceral holloworgans.

In one embodiment, the system comprises an impedance catheter capable ofbeing introduced into a treatment site, a solution delivery source forinjecting a solution through the catheter into the treatment site, aconstant current source enabling the supply of constant electricalcurrent to the treatment site, and a data acquisition system enablingthe measurement of parallel conductance at the treatment site, wherebyenabling calculation of cross-sectional area at the treatment site.

In one embodiment, the catheter further comprises an inflatable balloonalong its longitudinal axis.

In one embodiment, the catheter further comprises a pressure transducernear the distal end of the catheter.

In one approach, a method of measuring the cross-sectional area of atargeted treatment site comprises: introducing an impedance catheterinto a treatment site; providing constant electrical current to thetreatment site; injecting a first solution of first compound; measuringa first conductance value at the treatment site; injecting a secondsolution of a second compound; measuring a second conductance value atthe treatment site; calculating the cross-sectional area of thetreatment site based on the first and second conductance values and theconductivities of the first and second compounds.

In one approach, a method of constructing a three-dimensional model of atreatment site that comprises: introducing an impedance catheter into atreatment site; measuring a first cross-sectional area at a first point;adjusting the position of the catheter; measuring a secondcross-sectional area at a second point, and so on; constructing athree-dimensional model of the treatment site along the longitudinalaxis based on multiple longitudinal cross-sectional area measurements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a balloon catheter having impedance measuringelectrodes supported in front of the stenting balloon;

FIG. 1B illustrates a balloon catheter having impedance measuringelectrodes within and in front of the balloon;

FIG. 1C illustrates a catheter having an ultrasound transducer withinand in front of balloon;

FIG. 1D illustrates a catheter without a stenting balloon;

FIG. 1E illustrates a guide catheter with wire and impedance electrodes;

FIG. 1F illustrates a catheter with multiple detection electrodes;

FIG. 2A illustrates a catheter in cross-section proximal to the locationof the sensors showing the leads embedded in the material of the probe;

FIG. 2B illustrates a catheter in cross-section proximal to the locationof the sensors showing the leads run in separate lumens;

FIG. 3 is a schematic of one embodiment of the system showing a cathetercarrying impedance measuring electrodes connected to the dataacquisition equipment and excitation unit for the cross-sectional areameasurement;

FIG. 4A show the detected filtered voltage drop as measured in the bloodstream before and after injection of 1.5% NaCl solution;

FIG. 4B shows the peak-to-peak envelope of the detected voltage shown inFIG. 4A;

FIG. 5A show the detected filtered voltage drop as measured in the bloodstream before and after injection of 0.5% NaCl solution;

FIG. 5B shows the peak-to-peak envelope of the detected voltage shown inFIG. 5A;

FIG. 6 illustrates balloon distension of the lumen of the coronaryartery;

FIG. 7 illustrates balloon distension of a stent into the lumen of thecoronary artery;

FIG. 8A illustrates the voltage recorded by a conductance catheter witha radius of 0.55 mm for various size vessels (vessel radii of 3.1, 2.7,2.3, 1.9, 1.5 and 0.55 mm for the six curves, respectively) when a 0.5%NaCl bolus is injected into the treatment site; and

FIG. 8B illustrates the voltage recorded by a conductance catheter witha radius of 0.55 mm for various size vessels (vessel radii of 3.1, 2.7,2.3, 1.9, 1.5 and 0.55 mm for the six curves, respectively) when a 1.5%NaCl bolus is injected into the treatment site.

DETAILED DESCRIPTION

The present disclosure includes disclosure to make accurate measures ofthe luminal cross-sectional area of organ stenosis within acceptablelimits to enable accurate and scientific stent sizing and placement inorder to improve clinical outcomes by avoiding under or over deploymentand under or over sizing of a stent which can cause acute closure orin-stent re-stenosis. In one embodiment, an angioplasty or stent balloonincludes impedance electrodes supported by the catheter in front of theballoon. These electrodes enable the immediate measurement of thecross-sectional area of the vessel during the balloon advancement. Thisprovides a direct measurement of non-stenosed area and allows theselection of the appropriate stent size. In one approach, error due tothe loss of current in the wall of the organ and surrounding tissue iscorrected by injection of two solutions of NaCl or other solutions withknown conductivities. In another embodiment impedance electrodes arelocated in the center of the balloon in order to deploy the stent to thedesired cross-sectional area. These embodiments and proceduressubstantially improve the accuracy of stenting and the outcome andreduce the cost.

Other embodiments make diagnosis of valve stenosis more accurate andmore scientific by providing a direct accurate measurement ofcross-sectional area of the valve annulus, independent of the flowconditions through the valve. Other embodiments improve evaluation ofcross-sectional area and flow in organs like the gastrointestinal tractand the urinary tract.

Embodiments of the present disclosure overcome the problems associatedwith determination of the size (cross-sectional area) of luminal organs,such as, for example, in the coronary arteries, carotid, femoral, renaland iliac arteries, aorta, gastrointestinal tract, urethra and ureter.Embodiments also provide methods for registration of acute changes inwall conductance, such as, for example, due to edema or acute damage tothe tissue, and for detection of muscle spasms/contractions.

As described below, in one preferred embodiment, there is provided anangioplasty catheter with impedance electrodes near the distal end 19 ofthe catheter (i.e., in front of the balloon) for immediate measurementof the cross-sectional area of a vessel lumen during balloonadvancement. This catheter includes electrodes for accurate detection oforgan luminal cross-sectional area and ports for pressure gradientmeasurements. Hence, it is not necessary to change catheters such aswith the current use of intravascular ultrasound. In one preferredembodiment, the catheter provides direct measurement of the non-stenosedarea, thereby allowing the selection of an appropriately sized stent. Inanother embodiment, additional impedance electrodes may be incorporatedin the center of the balloon on the catheter in order to deploy thestent to the desired cross-sectional area. The procedures describedherein substantially improve the accuracy of stenting and improve thecost and outcome as well.

In another embodiment, the impedance electrodes are embedded within acatheter to measure the valve area directly and independent of cardiacoutput or pressure drop and therefore minimize errors in the measurementof valve area. Hence, measurements of area are direct and not based oncalculations with underlying assumptions. In another embodiment,pressure sensors can be mounted proximal and distal to the impedanceelectrodes to provide simultaneous pressure gradient recording.

Devices

We designed and build the impedance or conductance catheters illustratedin FIGS. 1A-1F. With reference to the exemplary embodiment shown in FIG.1A, four wires were threaded through one of the 2 lumens of a 4 Frcatheter. Here, electrodes 26 and 28, are spaced 1 mm apart and form theinner (detection) electrodes. Electrodes 25 and 27 are spaced 4-5 mmfrom either side of the inner electrodes and form the outer (excitation)electrodes.

In one approach, dimensions of a catheter to be used for any givenapplication depend on the optimization of the potential field usingfinite element analysis described below. For small organs or inpediatric patients the diameter of the catheter may be as small as 0.3mm. In large organs the diameter may be significantly larger dependingon the results of the optimization based on finite element analysis. Theballoon size will typically be sized according to the preferreddimension of the organ after the distension. The balloon may be made ofmaterials, such as, for example, polyethylene, latex,polyestherurethane, or combinations thereof. The thickness of theballoon will typically be on the order of a few microns. The catheterwill typically be made of PVC or polyethylene, though other materialsmay equally well be used. The excitation and detection electrodestypically surround the catheter as ring electrodes but they may also bepoint electrodes or have other suitable configurations. These electrodesmay be made of any conductive material, preferably of platinum iridiumor a carbon-coasted surface to avoid fibrin deposits. In the preferredembodiment, the detection electrodes are spaced with 0.5-1 mm betweenthem and with a distance between 4-7 mm to the excitation electrodes onsmall catheters. The dimensions of the catheter selected for a treatmentdepend on the size of the vessel and are preferably determined in parton the results of finite element analysis, described below. On largecatheters, for use in larger vessels and other visceral hollow organs,the electrode distances may be larger.

Referring to FIGS. 1A, 1B, 1C and 1D, several embodiments of thecatheters are illustrated. The catheters shown contain to a varyingdegree different electrodes, number and optional balloon(s). Withreference to the embodiment shown in FIG. 1A, there is shown animpedance catheter 20 with 4 electrodes 25, 26, 27 and 28 placed closeto the tip 19 of the catheter. Proximal to these electrodes is anangiography or stenting balloon 30 capable of being used for treatingstenosis. Electrodes 25 and 27 are excitation electrodes, whileelectrodes 26 and 28 are detection electrodes, which allow measurementof cross-sectional area during advancement of the catheter, as describedin further detail below. The portion of the catheter 20 within balloon30 includes an infusion port 35 and a pressure port 36.

The catheter 20 may also advantageously include several miniaturepressure transducers (not shown) carried by the catheter or pressureports for determining the pressure gradient proximal at the site wherethe cross-sectional area is measured. The pressure is preferablymeasured inside the balloon and proximal, distal to and at the locationof the cross-sectional area measurement, and locations proximal anddistal thereto, thereby enabling the measurement of pressure recordingsat the site of stenosis and also the measurement of pressure-differencealong or near the stenosis. In one embodiment, shown in FIG. 1A,Catheter 20 advantageously includes pressure port 90 and pressure port91 proximal to or at the site of the cross-sectional measurement forevaluation of pressure gradients. As described below with reference toFIGS. 2A, 2B and 3, in one embodiment, the pressure ports are connectedby respective conduits in the catheter 20 to pressure sensors in thedata acquisition system 100. Such pressure sensors are well known in theart and include, for example, fiber-optic systems, miniature straingauges, and perfused low-compliance manometry.

In one embodiment, a fluid-filled silastic pressure-monitoring catheteris connected to a pressure transducer. Luminal pressure can be monitoredby a low compliance external pressure transducer coupled to the infusionchannel of the catheter. Pressure transducer calibration was carried outby applying 0 and 100 mmHg of pressure by means of a hydrostatic column.

In one embodiment, shown in FIG. 1B, the catheter 39 includes anotherset of excitation electrodes 40, 41 and detection electrodes 42, 43located inside the angioplastic or stenting balloon 30 for accuratedetermination of the balloon cross-sectional area during angioplasty orstent deployment. These electrodes are in addition to electrodes 25, 26,27 and 28.

In one embodiment, the cross-sectional area may be measured using atwo-electrode system. In another embodiment, illustrated in FIG. 1F,several cross-sectional areas can be measured using an array of 5 ormore electrodes. Here, the excitation electrodes 51, 52, are used togenerate the current while detection electrodes 53, 54, 55, 56 and 57are used to detect the current at their respective sites.

The tip of the catheter can be straight, curved or with an angle tofacilitate insertion into the coronary arteries or other lumens, suchas, for example, the biliary tract. The distance between the balloon andthe electrodes is usually small, in the 0.5-2 cm range but can be closeror further away, depending on the particular application or treatmentinvolved.

In another embodiment, shown in FIG. 1C the catheter 21 has one or moreimaging or recording device, such as, for example, ultrasoundtransducers 50 for cross-sectional area and wall thickness measurements.As shown in this embodiment, the transducers 50 are located near thedistal tip 19 of the catheter 21.

FIG. 1D illustrates an embodiment of the impedance catheter 22 withoutan angioplastic or stenting balloon. This catheter also possesses aninfusion or injection port 35 located proximal relative to theexcitation electrode 25 and pressure port 36.

With reference to the embodiment shown in FIG. 1E, the electrodes 25,26, 27, 28 can also be built onto a wire 18, such as, for example, apressure wire, and inserted through a guide catheter 23 where theinfusion of bolus can be made through the lumen of the guide catheter37.

With reference to the embodiments shown in FIGS. 1A, 1B, 1C, 1D, 1E and1F, the impedance catheter advantageously includes optional ports 35,36, 37 for suction of contents of the organ or infusion of fluid. Thesuction/infusion port 35, 36, 37 can be placed as shown with the balloonor elsewhere both proximal or distal to the balloon on the catheter. Thefluid inside the balloon can be any biologically compatible conductingfluid. The fluid to inject through the infusion port or ports can be anybiologically compatible fluid but the conductivity of the fluid isselected to be different from that of blood (e.g., NaCl).

In another embodiment (not illustrated), the catheter contains an extrachannel for insertion of a guide wire to stiffen the flexible catheterduring the insertion or data recording. In yet another embodiment (notillustrated), the catheter includes a sensor for measurement of the flowof fluid in the body organ.

Systems for Determining Cross-Sectional Areas and Pressure Gradients

The operation of the impedance catheter 20 is as follows:

With reference to the embodiment shown in FIG. 1A for electrodes 25, 26,27, 28, conductance of current flow through the organ lumen and organwall and surrounding tissue is parallel; i.e.,

$\begin{matrix}{{G\left( {z,t} \right)} = {\frac{{{CSA}\left( {z,t} \right)} \cdot C_{b}}{L} + {G_{p}\left( {z,t} \right)}}} & \left\lbrack {1a} \right\rbrack\end{matrix}$where G_(p)(z,t) is the effective conductance of the structure outsidethe bodily fluid (organ wall and surrounding tissue), and C_(b) is thespecific electrical conductivity of the bodily fluid which for bloodgenerally depends on the temperature, hematocrit and orientation anddeformation of blood cells and L is the distance between the detectionelectrodes. Equation 1 can be rearranged to solve for cross sectionalarea CSA(t), with a correction factor, α, if the electric field isnon-homogeneous, as

$\begin{matrix}{{{CSA}\left( {z,t} \right)} = {\frac{L}{\alpha\; C_{b}}\left\lbrack {{G\left( {z,t} \right)} - {G_{p}\left( {z,t} \right)}} \right\rbrack}} & \left\lbrack {1b} \right\rbrack\end{matrix}$where α would be equal to 1 if the field were completely homogeneous.The parallel conductance, G_(p), is an offset error that results fromcurrent leakage. G_(p) would equal 0 if all of the current were confinedto the blood and hence would correspond to the cylindrical model givenby Equation [10]. In one approach, finite element analysis is used toproperly design the spacing between detection and excitation electrodesrelative to the dimensions of the vessel to provide a nearly homogenousfield such that a can be considered equal to 1. Our simulations showthat a homogenous or substantially homogenous field is provided by (1)the placement of detection electrodes substantially equidistant from theexcitation electrodes and (2) maintaining the distance between thedetection and excitation electrodes substantially comparable to thevessel diameter. In one approach, a homogeneous field is achieved bytaking steps (1) and/or (2) described above so that α is equals 1 in theforegoing analysis.

At any given position, z, along the long axis of organ and at any giventime, t, in the cardiac cycle, G_(p) is a constant. Hence, twoinjections of different concentrations and/or conductivities of NaClsolution give rise to two equations:C ₁·CSA(z,t)+L·G _(p)(z,t)=L·G ₁(z,t)  [2]andC ₂·CSA(z,t)+L·G _(p)(z,t)=L·G ₂(z,t)  [3]which can be solved simultaneously for CSA and G_(p) as

$\begin{matrix}{{{{CSA}\left( {z,t} \right)} = {L\frac{\left\lbrack {{G_{2}\left( {z,t} \right)} - {G_{1}\left( {z,t} \right)}} \right\rbrack}{\left\lbrack {C_{2} - C_{1}} \right\rbrack}}}{and}} & \lbrack 4\rbrack \\{{G_{p}\left( {z,t} \right)} = \frac{\left\lbrack {{C_{2} \cdot {G_{1}\left( {z,t} \right)}} - {C_{1} \cdot {G_{2}\left( {z,t} \right)}}} \right\rbrack}{\left\lbrack {C_{2} - C_{1}} \right\rbrack}} & \lbrack 5\rbrack\end{matrix}$where subscript “1” and subscript “2” designate any two injections ofdifferent NaCl concentrations and/or conductivities. For each injectionk, C_(k) gives rise to G_(k) which is measured as the ratio of the rootmean square of the current divided by the root mean square of thevoltage. The C_(k) is typically determined through in vitro calibrationfor the various NaCl concentrations and/or conductivities. Theconcentration of NaCl used is typically on the order of 0.45 to 1.8%.The volume of NaCl solution is typically about 5 ml, but sufficient todisplace the entire local vascular blood volume momentarily. The valuesof CSA(t) and G_(p)(t) can be determined at end-diastole or end-systole(i.e., the minimum and maximum values) or the mean thereof.

Once the CSA and G_(p) of the vessel are determined according to theabove embodiment, rearrangement of equation [1] allows the calculationof the specific electrical conductivity of blood in the presence ofblood blow as

$\begin{matrix}{C_{b} = {\frac{L}{{CSA}\left( {z,t} \right)}\left\lbrack {{G\left( {z,t} \right)} - {G_{p}\left( {z,t} \right)}} \right\rbrack}} & \lbrack 6\rbrack\end{matrix}$In this way, equation [1b] can be used to calculate the CSA continuously(temporal variation as for example through the cardiac cycle) in thepresence of blood.

In one approach, a pull or push through is used to reconstruct thevessel along its length. During a long injection (e.g., 10-15 s), thecatheter can be pulled back or pushed forward at constant velocity U.Equation [1b] can be expressed as

$\begin{matrix}{{{CSA}\left( {{U \cdot t},t} \right)} = {\frac{L}{C_{b}}\left\lbrack {{G\left( {{U \cdot t},t} \right)} - {G_{p}\left( {U \cdot \left( {t,t} \right)} \right\rbrack}} \right.}} & \lbrack 7\rbrack\end{matrix}$where the axial position, z, is the product of catheter velocity, U, andtime, t; i.e., z=U·t.

For the two injections, denoted by subscript “1” and subscript “2”,respectively, we can consider different time points T1, T2, etc. suchthat equation [7] can be written as

$\begin{matrix}{{{CSA}_{1}\left( {{U \cdot T_{1}},t} \right)} = {\frac{L}{C_{1}}\left\lbrack {{G_{1}\left( {{U \cdot T_{1}},t} \right)} - {G_{p\; 1}\left( {{U \cdot T_{1}},t} \right)}} \right\rbrack}} & \left\lbrack {8a} \right\rbrack \\{{{{CSA}_{1}\left( {{U \cdot T_{1}},t} \right)} = {\frac{L}{C_{2}}\left\lbrack {{G_{2}\left( {{U \cdot T_{1}},t} \right)} - {G_{p\; 1}\left( {{U \cdot T_{1}},t} \right)}} \right\rbrack}}{and}} & \left\lbrack {8b} \right\rbrack \\{{{CSA}_{2}\left( {{U \cdot T_{2}},t} \right)} = {\frac{L}{C_{I}}\left\lbrack {{G_{1}\left( {{U \cdot T_{2}},t} \right)} - {G_{p\; 2}\left( {{U \cdot T_{2}},t} \right)}} \right\rbrack}} & \left\lbrack {9a} \right\rbrack \\{{{CSA}_{2}\left( {{U \cdot T_{2}},t} \right)} = {\frac{L}{C_{2}}\left\lbrack {{G_{2}\left( {{U \cdot T_{2}},t} \right)} - {G_{p\; 2}\left( {{U \cdot T_{2}},t} \right)}} \right\rbrack}} & \left\lbrack {9b} \right\rbrack\end{matrix}$and so on. Each set of equations [8a], [8b] and [9a], [9b], etc. can besolved for CSA₁, G_(p1) and CSA₂, G_(p2), respectively. Hence, we canmeasure the CSA at various time intervals and hence of differentpositions along the vessel to reconstruct the length of the vessel. Inone embodiment, the data on the CSA and parallel conductance as afunction of longitudinal position along the vessel can be exported froman electronic spreadsheet, such as, for example, an Excel file, toAutoCAD where the software uses the coordinates to render a3-Dimensional vessel on the monitor.

For example, in one exemplary approach, the pull back reconstruction wasmade during a long injection where the catheter was pulled back atconstant rate by hand. The catheter was marked along its length suchthat the pull back was made at 2 mm/sec. Hence, during a 10 secondinjection, the catheter was pulled back about 2 cm. The data wascontinuously measured and analyzed at every two second interval; i.e.,at every 4 mm. Hence, six different measurements of CSA and G_(p) weremade which were used to reconstruction the CSA and G_(p) along thelength of the 2 cm segment.

Operation of the Impedance Catheter 39:

With reference to the embodiment shown in FIG. 1B, the voltagedifference between the detection electrodes 42 and 43 depends on themagnitude of the current (I) multiplied by the distance (D) between thedetection electrodes and divided by the conductivity (C) of the fluidand the cross-sectional area (CSA) of the artery or other organs intowhich the catheter is introduced. Since the current (I), the distance(L) and the conductivity (C) normally can be regarded as calibrationconstants, an inverse relationship exists between the voltage differenceand the CSA as shown by the following equations:

$\begin{matrix}{{{\Delta\; V} = \frac{I \cdot L}{C \cdot {CSA}}}{or}} & \left\lbrack {10a} \right\rbrack \\{{CSA} = \frac{G \cdot L}{C}} & \left\lbrack {10b} \right\rbrack\end{matrix}$where G is conductance expressed as the ratio of current to voltage(I/ΔV). Equation [10] is identical to equation [1b] if we neglect theparallel conductance through the vessel wall and surrounding tissuebecause the balloon material acts as an insulator. This is thecylindrical model on which the conductance method is used.

As described below with reference to FIGS. 2A, 2B, 3, 4 and 5, theexcitation and detection electrodes are electrically connected toelectrically conductive leads in the catheter for connecting theelectrodes to the data acquisition system 100.

FIGS. 2A and 2B illustrate two embodiments 20A and 20B of the catheterin cross-section. Each embodiment has a lumen 60 for inflating anddeflating the balloon and a lumen 61 for suction and infusion. The sizesof these lumens can vary in size. The impedance electrode electricalleads 70A are embedded in the material of the catheter in the embodimentin FIG. 2A, whereas the electrode electrical leads 70B are tunneledthrough a lumen 71 formed within the body of catheter 70B in FIG. 2B.

Pressure conduits for perfusion manometry connect the pressure ports 90,91 to transducers included in the data acquisition system 100. As shownin FIG. 2A pressure conduits 95A may be formed in 20A. In anotherembodiment, shown in FIG. 2B, pressure conduits 95B constituteindividual conduits within a tunnel 96 formed in catheter 20B. In theembodiment described above where miniature pressure transducers arecarried by the catheter, electrical conductors will be substituted forthese pressure conduits.

With reference to FIG. 3, in one embodiment, the catheter 20 connects toa data acquisition system 100, to a manual or automatic system 105 fordistension of the balloon and to a system 106 for infusion of fluid orsuction of blood. The fluid will be heated to 37-39° or equivalent tobody temperature with heating unit 107. The impedance planimetry systemtypically includes a constant current unit, amplifiers and signalconditioners. The pressure system typically includes amplifiers andsignal conditioners. The system can optionally contain signalconditioning equipment for recording of fluid flow in the organ.

In one preferred embodiment, the system is pre-calibrated and the probeis available in a package. Here, the package also preferably containssterile syringes with the fluids to be injected. The syringes areattached to the machine and after heating of the fluid by the machineand placement of the probe in the organ of interest, the user presses abutton that initiates the injection with subsequent computation of thedesired parameters. The CSA and parallel conductance and other relevantmeasures such as distensibility, tension, etc. will typically appear onthe display panel in the PC module 160. Here, the user can then removethe stenosis by distension or by placement of a stent.

If more than one CSA is measured, the system can contain a multiplexerunit or a switch between CSA channels. In one embodiment, each CSAmeasurement will be through separate amplifier units. The same mayaccount for the pressure channels.

In one embodiment, the impedance and pressure data are analog signalswhich are converted by analog-to-digital converters 150 and transmittedto a computer 160 for on-line display, on-line analysis and storage. Inanother embodiment, all data handling is done on an entirely analogbasis. The analysis advantageously includes software programs forreducing the error due to conductance of current in the organ wall andsurrounding tissue and for displaying the 2D or 3D-geometry of the CSAdistribution along the length of the vessel along with the pressuregradient. In one embodiment of the software, a finite element approachor a finite difference approach is used to derive the CSA of the organstenosis taking parameters such as conductivities of the fluid in theorgan and of the organ wall and surrounding tissue into consideration.In another embodiment, simpler circuits are used; e.g., based on makingtwo or more injections of different NaCl solutions to vary theresistivity of fluid in the vessel and solving the two simultaneousequations [2] and [3] for the CSA and parallel conductance (equations[4] and [5], respectively). In another embodiment, the software containsthe code for reducing the error in luminal CSA measurement by analyzingsignals during interventions such as infusion of a fluid into the organor by changing the amplitude or frequency of the current from theconstant current amplifier. The software chosen for a particularapplication, preferably allows computation of the CSA with only a smallerror instantly or within acceptable time during the medical procedure.

In one approach, the wall thickness is determined from the parallelconductance for those organs that are surrounded by air ornon-conducting tissue. In such cases, the parallel conductance is equalto

$\begin{matrix}{G_{p} = \frac{{CSA}_{w} \cdot C_{w}}{L}} & \left\lbrack {11a} \right\rbrack\end{matrix}$where CSAW is the wall area of the organ and C_(w) is the electricalconductivity through the wall. This equation can be solved for the wallCSA_(W) as

$\begin{matrix}{{CSA}_{w} = \frac{G_{p} \cdot L}{C_{w}}} & \left\lbrack {11b} \right\rbrack\end{matrix}$For a cylindrical organ, the wall thickness, h, can be expressed as

$\begin{matrix}{h = \frac{{CSA}_{w}}{\pi\; D}} & \lbrack 12\rbrack\end{matrix}$where D is the diameter of the vessel which can be determined from thecircular CSA (D=[4CSA/π]^(1/2)).

When the CSA, pressure, wall thickness, and flow data are determinedaccording to the embodiments outlined above, it is possible to computethe compliance (e.g., ΔCSA/ΔP), tension (e.g., P·r, where P and r arethe intraluminal pressure and radius of a cylindrical organ), stress(e.g., P·r/h where h is the wall thickness of the cylindrical organ),strain (e.g., (C−C_(d))/C_(d) where C is the inner circumference andC_(d) is the circumference in diastole) and wall shear stress (e.g., 4μQ/r³ where μ, Q and r are the fluid viscosity, flow rate and radius ofthe cylindrical organ for a fully developed flow). These quantities canbe used in assessing the mechanical characteristics of the system inhealth and disease.

Methods

In one approach, luminal cross-sectional area is measured by introducinga catheter from an exteriorly accessible opening (e.g., mouth, nose oranus for GI applications; or e.g., mouth or nose for airwayapplications) into the hollow system or targeted luminal organ. Forcardiovascular applications, the catheter can be inserted into theorgans in various ways; e.g., similar to conventional angioplasty. Inone embodiment, an 18 gauge needle is inserted into the femoral arteryfollowed by an introducer. A guide wire is then inserted into theintroducer and advanced into the lumen of the femoral artery. A 4 or 5Fr conductance catheter is then inserted into the femoral artery viawire and the wire is subsequently retracted. The catheter tip containingthe conductance electrodes can then be advanced to the region ofinterest by use of x-ray (i.e., fluoroscopy). In another approach, thismethodology is used on small to medium size vessels (e.g., femoral,coronary, carotid, iliac arteries, etc.).

In one approach, a minimum of two injections (with differentconcentrations and/or conductivities of NaCl) are required to solve forthe two unknowns, CSA and G_(p). In another approach, three injectionswill yield three set of values for CSA and G_(p) (although notnecessarily linearly independent), while four injections would yield sixset of values. In one approach, at least two solutions (e.g., 0.5% and1.5% NaCl solutions) are injected in the targeted luminal organ orvessel. Our studies indicate that an infusion rate of approximately 1ml/s for a five second interval is sufficient to displace the bloodvolume and results in a local pressure increase of less than 10 mmHg inthe coronary artery. This pressure change depends on the injection ratewhich should be comparable to the organ flow rate.

In one preferred approach, involving the application of Equations [4]and [5], the vessel is under identical or very similar conditions duringthe two injections. Hence, variables, such as, for example, the infusionrate, bolus temperature, etc., are similar for the two injections.Typically, a short time interval is to be allowed (1-2 minute period)between the two injections to permit the vessel to return to homeostaticstate. This can be determined from the baseline conductance as shown inFIG. 4 or 5. The parallel conductance is preferably the same or verysimilar during the two injections. In one approach, dextran, albumin oranother large molecular weight molecule can be added to the NaClsolutions to maintain the colloid osmotic pressure of the solution toreduce or prevent fluid or ion exchange through the vessel wall.

In one approach, the NaCl solution is heated to body temperature priorto injection since the conductivity of current is temperature dependent.In another approach, the injected bolus is at room temperature, but atemperature correction is made since the conductivity is related totemperature in a linear fashion.

In one approach, a sheath is inserted either through the femoral orcarotid artery in the direction of flow. To access the lower anteriordescending (LAD) artery, the sheath is inserted through the ascendingaorta. For the carotid artery, where the diameter is typically on theorder of 5-5.5 mm, a catheter having a diameter of 1.9 mm can be used,as determined from finite element analysis, discussed further below. Forthe femoral and coronary arteries, where the diameter is typically inthe range from 3.5-4 mm, so a catheter of about 0.8 mm diameter would beappropriate. The catheter can be inserted into the femoral, carotid orLAD artery through a sheath appropriate for the particular treatment.Measurements for all three vessels can be made similarly.

Described here are the protocol and results for one exemplary approachthat is generally applicable to most arterial vessels. The conductancecatheter was inserted through the sheath for a particular vessel ofinterest. A baseline reading of voltage was continuously recorded. Twocontainers containing 0.5% and 1.5% NaCl were placed in temperature bathand maintained at 37°. A 5-10 ml injection of 1.5% NaCl was made over a5 second interval. The detection voltage was continuously recorded overa 10 second interval during the 5 second injection. Several minuteslater, a similar volume of 1.5% NaCl solution was injected at a similarrate. The data was again recorded. Matlab was used to analyze the dataincluding filtering with high pass and with low cut off frequency (1200Hz). The data was displayed using Matlab and the mean of the voltagesignal during the passage of each respective solution was recorded. Thecorresponding currents were also measured to yield the conductance(G=I/V). The conductivity of each solution was calibrated with sixdifferent tubes of known CSA at body temperature. A model using equation[10] was fitted to the data to calculate conductivity C. The analysiswas carried out in SPSS using the non-linear regression fit. Given C andG for each of the two injections, an excel sheet file was formatted tocalculate the CSA and Gp as per equations [4] and [5], respectively.These measurements were repeated several times to determine thereproducibility of the technique. The reproducibility of the data waswithin 5%. Ultrasound (US) was used to measure the diameter of thevessel simultaneous with our conductance measurements. The detectionelectrodes were visualized with US and the diameter measurements wasmade at the center of the detection electrodes. The maximum differencesbetween the conductance and US measurements were within 10%.

FIGS. 4A, 4B, 5A and 5B illustrate voltage measurements in the bloodstream in the left carotid artery. Here, the data acquisition had a thesampling frequency of 75 KHz, with two channels—the current injected andthe detected voltage, respectively. The current injected has a frequencyof 5 KH, so the voltage detected, modulated in amplitude by theimpedance changing through the bolus injection will have a spectrum inthe vicinity of 5 KHz.

With reference to FIG. 4A there is shown a signal processed with a highpass filter with low cut off frequency (1200 Hz). The top and bottomportions 200, 202 show the peak-to-peak envelope detected voltage whichis displayed in FIG. 4B (bottom). The initial 7 seconds correspond tothe baseline; i.e., electrodes in the blood stream. The next 7 secondscorrespond to an injection of hyper-osmotic NaCl solution (1.5% NaCl).It can be seen that the voltage is decreased implying increaseconductance (since the injected current is constant). Once the NaClsolution is washed out, the baseline is recovered as can be seen in thelast portion of the FIGS. 4A and 4B. FIGS. 5A and 5B shows similar datacorresponding to 0.5% NaCl solutions.

The voltage signals are ideal since the difference between the baselineand the injected solution is apparent and systematic. Furthermore, thepulsation of vessel diameter can be seen in the 0.5% and 1.5% NaClinjections (FIGS. 4 and 5, respectively). This allows determination ofthe variation of CSA throughout the cardiac cycle as outline above.

The NaCl solution can be injected by hand or by using a mechanicalinjector to momentarily displace the entire volume of blood or bodilyfluid in the vessel segment of interest. The pressure generated by theinjection will not only displace the blood in the antegrade direction(in the direction of blood flow) but also in the retrograde direction(momentarily push the blood backwards). In other visceral organs whichmay be normally collapsed, the NaCl solution will not displace blood asin the vessels but will merely open the organs and create a flow of thefluid. In one approach, after injection of a first solution into thetreatment or measurement site, sensors monitor and confirm baseline ofconductance prior to injection of a second solution into the treatmentsite.

The injections described above are preferably repeated at least once toreduce errors associated with the administration of the injections, suchas, for example, where the injection does not completely displace theblood or where there is significant mixing with blood. It will beunderstood that any bifurcation(s) (with branching angle near 90degrees) near the targeted luminal organ can cause an overestimation ofthe calculated CSA. Hence, generally the catheter should be slightlyretracted or advanced and the measurement repeated. An additionalapplication with multiple detection electrodes or a pull back or pushforward during injection will accomplish the same goal. Here, an arrayof detection electrodes can be used to minimize or eliminate errors thatwould result from bifurcations or branching in the measurement ortreatment site.

In one approach, error due to the eccentric position of the electrode orother imaging device can be reduced by inflation of a balloon on thecatheter. The inflation of balloon during measurement will place theelectrodes or other imaging device in the center of the vessel away fromthe wall. In the case of impedance electrodes, the inflation of ballooncan be synchronized with the injection of bolus where the ballooninflation would immediately precede the bolus injection. Our results,however, show that the error due to catheter eccentricity is small.

The CSA predicted by Equation [4] corresponds to the area of the vesselor organ external to the catheter (i.e., CSA of vessel minus CSA ofcatheter). If the conductivity of the NaCl solutions is determined bycalibration from Equation [10] with various tubes of known CSA, then thecalibration accounts for the dimension of the catheter and thecalculated CSA corresponds to that of the total vessel lumen as desired.In one embodiment, the calibration of the CSA measurement system will beperformed at 37° C. by applying 100 mmHg in a solid polyphenolenoxideblock with holes of known CSA ranging from 7.065 mm² (3 mm in diameter)to 1017 mm² (36 in mm). If the conductivity of the solutions is obtainedfrom a conductivity meter independent of the catheter, however, then theCSA of the catheter is generally added to the CSA computed from Equation[4] to give the desired total CSA of the vessel.

The signals are generally non-stationary, nonlinear and stochastic. Todeal with non-stationary stochastic functions, one can use a number ofmethods, such as the Spectrogram, the Wavelet's analysis, theWigner-Ville distribution, the Evolutionary Spectrum, Modal analysis, orpreferably the intrinsic model function (IMF) method. The mean orpeak-to-peak values can be systematically determined by theaforementioned signal analysis and used in Equation [4] to compute theCSA.

Referring to the embodiment shown in FIG. 6, the angioplasty balloon 30is shown distended within the coronary artery 150 for the treatment ofstenosis. As described above with reference to FIG. 1B, a set ofexcitation electrodes 40, 41 and detection electrodes 42, 43 are locatedwithin the angioplasty balloon 30. In another embodiment, shown in FIG.7, the angioplasty balloon 30 is used to distend the stent 160 withinblood vessel 150.

For valve area determination, it is not generally feasible to displacethe entire volume of the heart. Hence, the conductivity of blood ischanged by injection of hypertonic NaCl solution into the pulmonaryartery which will transiently change the conductivity of blood. If themeasured total conductance is plotted versus blood conductivity on agraph, the extrapolated conductance at zero conductivity corresponds tothe parallel conductance. In order to ensure that the two innerelectrodes are positioned in the plane of the valve annulus (2-3 mm), inone preferred embodiment, the two pressure sensors 36 are advantageouslyplaced immediately proximal and distal to the detection electrodes (1-2mm above and below, respectively) or several sets of detectionelectrodes (see, e.g., FIGS. 1D and 1F). The pressure readings will thenindicate the position of the detection electrode relative to the desiredsite of measurement (aortic valve: aortic-ventricular pressure; mitralvalve: left ventricular-atrial pressure; tricuspid valve: rightatrial-ventricular pressure; pulmonary valve: rightventricular-pulmonary pressure). The parallel conductance at the site ofannulus is generally expected to be small since the annulus consistsprimarily of collagen which has low electrical conductivity. In anotherapplication, a pull back or push forward through the heart chamber willshow different conductance due to the change in geometry and parallelconductance. This can be established for normal patients which can thenbe used to diagnose valvular stensosis.

In one approach, for the esophagus or the urethra, the procedures canconveniently be done by swallowing fluids of known conductances into theesophagus and infusion of fluids of known conductances into the urinarybladder followed by voiding the volume. In another approach, fluids canbe swallowed or urine voided followed by measurement of the fluidconductances from samples of the fluid. The latter method can be appliedto the ureter where a catheter can be advanced up into the ureter andfluids can either be injected from a proximal port on the probe (willalso be applicable in the intestines) or urine production can beincreased and samples taken distal in the ureter during passage of thebolus or from the urinary bladder.

In one approach, concomitant with measuring the cross-sectional area andor pressure gradient at the treatment or measurement site, a mechanicalstimulus is introduced by way of inflating the balloon or by releasing astent from the catheter, thereby facilitating flow through the stenosedpart of the organ. In another approach, concomitant with measuring thecross-sectional area and or pressure gradient at the treatment site, oneor more pharmaceutical substances for diagnosis or treatment of stenosisis injected into the treatment site. For example, in one approach, theinjected substance can be smooth muscle agonist or antagonist. In yetanother approach, concomitant with measuring the cross-sectional areaand or pressure gradient at the treatment site, an inflating fluid isreleased into the treatment site for release of any stenosis ormaterials causing stenosis in the organ or treatment site.

Again, it will be noted that the methods, systems, and cathetersdescribed herein can be applied to any body lumen or treatment site. Forexample, the methods, systems, and catheters described herein can beapplied to any one of the following exemplary bodily hollow systems: thecardiovascular system including the heart; the digestive system; therespiratory system; the reproductive system; and the urogential tract.

Finite Element Analysis:

In one preferred approach, finite element analysis (FEA) is used toverify the validity of Equations [4] and [5]. There are two majorconsiderations for the model definition: geometry and electricalproperties. The general equation governing the electric scalar potentialdistribution, V, is given by Poisson's equation as:∇·(C∇V)=−I  [13]where C, I and ∇ are the conductivity, the driving current density andthe del operator, respectively, Femlab or any standard finite elementpackages can be used to compute the nodal voltages using equation [13].Once V has been determined, the electric field can be obtained from asE=−∇V.

The FEA allows the determination of the nature of the field and itsalteration in response to different electrode distances, distancesbetween driving electrodes, wall thicknesses and wall conductivities.The percentage of total current in the lumen of the vessel (% I) can beused as an index of both leakage and field homogeneity. Hence, thevarious geometric and electrical material properties can be varied toobtain the optimum design; i.e., minimize the non-homogeneity of thefield. Furthermore, we simulated the experimental procedure by injectionof the two solutions of NaCl to verify the accuracy of equation [4].Finally, we assessed the effect of presence of electrodes and catheterin the lumen of vessel. The error terms representing the changes inmeasured conductance due to the attraction of the field to theelectrodes and the repulsion of the field from the resistive catheterbody were quantified.

We solved the Poisson's equation for the potential field which takesinto account the magnitude of the applied current, the location of thecurrent driving and detection electrodes, and the conductivities andgeometrical shapes in the model including the vessel wall andsurrounding tissue. This analysis suggest that the following conditionsare optimal for the cylindrical model: (1) the placement of detectionelectrodes equidistant from the excitation electrodes; (2) the distancebetween the current driving electrodes should be much greater than thedistance between the voltage sensing electrodes; and (3) the distancebetween the detection and excitation electrodes is comparable to thevessel diameter or the diameter of the vessel is small relative to thedistance between the driving electrodes. If these conditions aresatisfied, the equipotential contours more closely resemble straightlines perpendicular to the axis of the catheter and the voltage dropmeasured at the wall will be nearly identical to that at the center.Since the curvature of the equipotential contours is inversely relatedto the homogeneity of the electric field, it is possible to optimize thedesign to minimize the curvature of the field lines. Consequently, inone preferred approach, one or more of conditions (1)-(3) describedabove are met to increase the accuracy of the cylindrical model.

Theoretically, it is impossible to ensure a completely homogeneous fieldgiven the current leakage through the vessel wall into the surroundingtissue. We found that the iso-potential line is not constant as we moveout radially along the vessel as stipulated by the cylindrical model. Inone embodiment, we consider a catheter with a radius of 0.55 mm whosedetected voltage is shown in FIGS. 8A and 8B for two different NaClsolutions (0.5% and 1.5%, respectively). The origin corresponds to thecenter of the catheter. The first vertical line 220 represents the innerpart of the electrode which is wrapped around the catheter and thesecond vertical line 221 is the outer part of the electrode in contactwith the solution (diameter of electrode is approximately 0.25 mm). Thesix different curves, top to bottom, correspond to six different vesselswith radii of 3.1, 2.7, 2.3, 1.9, 1.5 and 0.55 mm, respectively. It canbe seen that a “hill” occurs at the detection electrode 220, 221followed by a fairly uniform plateau in the vessel lumen followed by anexponential decay into the surrounding tissue. Since the potentialdifference is measured at the detection electrode 220, 221, oursimulation generates the “hill” whose value corresponds to theequivalent potential in the vessel as used in Eq. [4]. Hence, for eachcatheter size, we varied the dimension of the vessel such that equation[4] is exactly satisfied. Consequently, we obtained the optimum cathetersize for a given vessel diameter such that the distributive modelsatisfies the lumped equations (Equation [4] and [5]). In this way, wecan generate a relationship between vessel diameter and catheterdiameter such that the error in the CSA measurement is less than 5%. Inone embodiment, different diameter catheters are prepackaged and labeledfor optimal use in certain size vessel. For example, for vesseldimension in the range of 4-5 mm, 5-7 mm or 7-10 mm, our analysis showsthat the optimum diameter catheters will be in the range of 0.91.4,1.4-2 or 2-4.6 mm, respectively. The clinician can select theappropriate diameter catheter based on the estimated vessel diameter ofinterest. This decision will be made prior to the procedure and willserve to minimize the error in the determination of lumen CSA.

While various embodiments of devices, systems, and methods for measuringcross-sectional areas and related calculations, have been described inconsiderable detail herein, the embodiments are merely offered by way ofnon-limiting examples of the disclosure described herein. It willtherefore be understood that various changes and modifications may bemade, and equivalents may be substituted for elements thereof, withoutdeparting from the scope of the disclosure. Indeed, this disclosure isnot intended to be exhaustive or to limit the scope of the disclosure.

Further, in describing representative embodiments, the disclosure mayhave presented a method and/or process as a particular sequence ofsteps. However, to the extent that the method or process does not relyon the particular order of steps set forth herein, the method or processshould not be limited to the particular sequence of steps described.Other sequences of steps may be possible. Therefore, the particularorder of the steps disclosed herein should not be construed aslimitations of the present disclosure. In addition, disclosure directedto a method and/or process should not be limited to the performance oftheir steps in the order written. Such sequences may be varied and stillremain within the scope of the present disclosure.

The invention claimed is:
 1. A method for measuring a cross-sectionalarea of and a fluid velocity at a targeted treatment site, the methodcomprising the steps of: introducing an impedance device into atreatment site, the impedance device comprising an elongated bodycomprising two detection electrodes positioned in between two excitationelectrodes, the impedance device selected from the group consisting ofan impedance catheter and an impedance wire; injecting a first solutionof a first compound having a first conductivity into the treatment site;measuring a first conductance value at the treatment site using theimpedance device, the first conductance value indicative of a bolus ofthe first solution; and, in either order, a) calculating across-sectional area of the treatment site based in part upon the firstconductivity of the first solution, the first conductance value, aconductivity of blood, and a known distance between the two detectionelectrodes of the impedance device; and b) measuring a velocity of fluidflow through the treatment site using the impedance device; wherein thetreatment site comprises a site selected from the group consisting of abody vessel, a biliary tract, a coronary artery, a carotid artery, afemoral artery, a renal artery, a iliac artery, a cerebral artery, andan aorta.
 2. The method of claim 1, further comprising the steps of:injecting a second solution of a second compound having a secondconductivity into the treatment site; and measuring a second conductancevalue at the treatment site using the impedance device, the secondconductance value indicative of a bolus of the second solution; andwherein the calculating step comprises calculating a size parameter ofthe treatment site based in part upon the first conductance value, thefirst conductivity of the first solution, the second conductance value,and the second conductivity of the second solution.
 3. The method ofclaim 2, wherein the first compound and the second compound are the samecompound.
 4. The method of claim 2, wherein the first compound and thesecond compound each comprise saline.
 5. The method of claim 2, whereinthe first conductivity does not equal the second conductivity.
 6. Themethod of claim 2, wherein the size parameter of the treatment site isselected from the group consisting of a cross-sectional area at thetreatment site and a diameter at the treatment site.
 7. The method ofclaim 1, further comprising the step of: inflating a balloon coupled tothe impedance device to breakup materials causing a stenosis at thetreatment site.
 8. The method of claim 7, further comprising the stepof: implanting a stent into the treatment site by inflating the balloon.9. The method of claim 8, wherein the balloon is inflated using a fluid,and the method further comprising the steps of: providing electricalcurrent into the fluid filling the balloon at various degrees of balloondistension; measuring a conductance of the fluid inside the balloon; andcalculating a size parameter of a lumen of the balloon.
 10. The methodof claim 1, further comprising the steps of: measuring a first pressuregradient at the treatment site using a pressure transducer coupled tothe impedance device; and calculating an additional size parameter ofthe treatment site based in part on the first pressure gradient.
 11. Themethod of claim 1, wherein the step of injecting the first solutiontemporarily displaces blood present at the treatment site.
 12. Themethod of claim 1, further comprising the steps of: selecting anappropriately-sized stent based on the calculated cross-sectional area;and implanting the stent into the treatment site.
 13. The method ofclaim 1, further comprising the step of: warming the first solutionprior to injection.
 14. The method of claim 1, further comprising thestep of: selecting an insertion device to be introduced into thetreatment site based upon the calculated cross-sectional area.
 15. Themethod of claim 14, wherein the insertion device comprises a ballooncatheter.